Inelastic scattering processes such as Brillouin scattering can often function in cascaded regimes and this is likely to occur in certain integrated opto-acoustic devices. We develop a Hamiltonian formalism for cascaded Brillouin scattering valid for both quantum and classical regimes. By regarding Brillouin scattering as the interaction of a single acoustic envelope and a single optical envelope that covers all Stokes and anti-Stokes orders, we obtain a compact model that is well suited for numerical implementation, extension to include other optical nonlinearities or short pulses, and application in the quantum-optics domain. We then theoretically analyze intra-mode forward Brillouin scattering (FBS) for arbitrary waveguides with and without optical dispersion. In the absence of optical dispersion, we find an exact analytical solution. With a perturbative approach, we furthermore solve the case of weak optical dispersion. Our work leads to several key results on intra-mode FBS. For negligible dispersion, we show that cascaded intra-mode FBS results in a pure phase modulation and discuss how this necessitates specific experimental methods for the observation of fibre-based and integrated FBS. Further, we discuss how the descriptions that have been established in these two classes of waveguides connect to each other and to the broader context of cavity opto-mechanics and Raman scattering. Finally, we draw an unexpected striking similarity between FBS and discrete diffraction phenomena in waveguide arrays, which makes FBS an interesting candidate for future research in quantum-optics.
We propose a method for generating cascaded forward Brillouin scattering (CFBS), based on a counter-propagated pump-probe technique, utilizing backward stimulated Brillouin scattering as its seed. The CFBS, induced by forward stimulated Brillouin scattering (FSBS), is generated via the energy transfer from the probe light to other acoustic resonance frequencies. Experimental results for the CFBS generated in a 390-m-long highly nonlinear fiber indicate that it has a high signal-to-noise ratio (SNR) and that the center frequencies of its acoustic resonance peaks agree with theoretical values. T…
We report the observation of stimulated Brillouin scattering and lasing at 1550~nm in barium fluoride (BaF$_2$) crystal. Brillouin lasing was achieved with ultra-high quality ($Q$) factor monolithic whispering gallery mode (WGM) mm-size disk resonators. Overmoded resonators were specifically used to provide cavity resonances for both the pump and all Brillouin Stokes waves. Single and multiple Brillouin Stokes radiations with frequency shift ranging from $8.2$ GHz up to $49$ GHz have been generated through cascaded Brillouin lasing. BaF$_2$ resonator-based Brillouin lasing can find potential a…
Cascaded stimulated Brillouin scattering (SBS) is a complex nonlinear optical process that results in the generation of several optical waves that are frequency shifted by an acoustic resonance frequency. Four-wave mixing (FWM) between these Brillouin shifted optical waves can create an equally spaced optical frequency comb with a stable spectral phase, i.e. a Brillouin frequency comb (BFC). Here, we investigate phase-locking of the spectral components of BFCs, considering FWM interactions arising from the Kerr-nonlinearity as well as from coupling by the acoustic field. Deriving for the first…
Storing and delaying optical signals plays a crucial role in data centers, phased array antennas, communication and future computing architectures. Here, we show a delay scheme based on cascaded Brillouin light storage, that achieves multi-stage delay at arbitrary positions within a photonic integrated circuit. Importantly these multiple resonant transfers between the optical and acoustic domain are controlled solely via external optical control pulses, allowing cascading of the delay without the need of aligning multiple structural resonances along the optical circuit.
The dynamics of cascaded-order Brillouin lasers make them ideal for applications such as rotation sensing, highly coherent optical communications, and low-noise microwave signal synthesis. Remark- ably, when implemented at the chip-scale, recent experimental studies have revealed that Brillouin lasers can operate in the fundamental linewidth regime where optomechanical and quantum noise sources dominate. To explore new opportunities for enhanced performance, we formulate a simple model to describe the physics of cascaded Brillouin lasers based on the coupled mode dynamics governed by electrost…
We present a novel approach to cascaded stimulated Brillouin scattering and frequency comb generation in which the multitude of interacting pump, Stokes, and anti-Stokes optical fields are described by a single forward wave and a single backward wave at a single carrier frequency. The envelopes of these two waves are modulated through coupling to a single acoustic oscillation and through four-wave mixing. Starting from a single pump field, we observe the emergence of a comb of frequencies as the intensity is increased. The set of three differential equations derived here are sufficient to desc…
Cascaded Brillouin scattering is increasingly becoming of interest in many areas of pho- tonics (e.g. see [1] and [2]) and has been studied experimentally by many groups. In gain assisted experiments for example up to nearly 800 distinct lines have been observed[3] while in passive cavities, mode locking of a few Brillouin lines has recently been demonstrated[4]. We show that although each pair of lines interact through the creation of an acoustic phonon the resulting acoustic field nevertheless can be written as the sum of only two waves (a forward and backward propagating wave). This new ana…
We present an experimental and theoretical study of cascaded high order Stimulated Brillouin Scatterings (SBS) in single mode fibers. It is shown that because of the back-scattering nature of the process, feedback in the input port is needed for obtaining a significant cascaded effect in nonresonant systems. We also discuss similarities to nonlinear photorefractive processes.
Due to their high circulating intensities, ultra-high quality factor dielectric whispering-gallery mode resonators have enabled the development of low threshold Raman microlasers. Subsequently, other Raman-related phenomena, such as cascaded stimulated Raman scattering (CSRS) and stimulated anti-Stokes Raman scattering (SARS), were observed. While low threshold frequency conversion and generation have clear applications, CSRS and SARS have been limited by the low Raman gain. In this work, the surface of a silica resonator is modified with an organic monolayer, increasing the Raman gain. Up to …
We formulate a generic concept of engineering optical modes and mechanical resonances in a pair of optically-coupled light-guiding membranes for achieving cascaded light scattering to multiple Stokes and anti-Stokes orders. By utilizing the light pressure exerted on the webs and their induced flexural vibrations, featuring flat phonon dispersion curve with a non-zero cut-off frequency, we show how to realize exact phase-matching between multiple successive optical side-bands. We predict continuous-wave generation of frequency combs for fundamental and high-order optical modes mediated via back…
In this paper, we prove theoretically that both the stimulated Stokes scattering and its reverse process can occur simultaneously for the light and acoustic waves at different points of the medium, resulting in transient and alternate energy flow between the pump and Stokes waves in the stimulated Brillouin scattering. Furthermore, it is found that stimulated Stokes scattering and its reverse process will dominate alternately on the whole during the three-wave coupling, but the eventual net energy flow must be from the pump wave to the Stokes wave as a result of the finite lifetime of acoustic…
In recent years, the manipulation of Fano resonances in the time domain has unlocked deep insights into a broad spectrum of systems' coherent dynamics. Here, inelastic scattering of light with coherent acoustic phonons is harnessed to achieve complex Fano resonances. The sudden change of phonon momentum during reflection leads to a transition from anti-Stokes to Stokes light scattering, producing two different resonances that interfere in the measurement process. We highlight the conditions necessary to achieve such interference, revealing an underlying symmetry between photons and phonons, an…
Photonic systems and technologies traditionally relegated to table-top experiments are poised to make the leap from the laboratory to real-world applications through integration. Stimulated Brillouin scattering (SBS) lasers, through their unique linewidth narrowing properties, are an ideal candidate to create highly-coherent waveguide integrated sources. In particular, cascaded-order Brillouin lasers show promise for multi-line emission, low-noise microwave generation and other optical comb applications. Photonic integration of these lasers can dramatically improve their stability to environme…
We report the first observation of stimulated Brillouin scattering (SBS) with Brillouin lasing, and Brillouin-coupled four-wave-mixing (FWM) in an ultra-high-Q silica microbottle resonator. The Brillouin lasing was observed at the frequency of $Ω_B=2π\times10.4$ GHz with a threshold power of $0.45$ mW. Coupling between Brillouin and FWM was observed in both backward and forward scattering directions with separations of $2Ω_B$. At a pump power of $10$ mW, FWM spacing reached to 7th and 9th order anti-Stokes and Stokes, respectively.
We present a technique to improve the slow-light performance of a side-coupled spaced sequence of resonators (SCISSOR) combined with a stimulated Brillouin scattering (SBS) gain medium in optical fiber. We evaluate device performance of SCISSOR-only and SCISSOR + SBS systems for different numbers of cascaded resonators from 1 to 70 using two different data fidelity metrics including eye-opening and mutual information. A practical system design is demonstrated by analyzing its performance in terms of fractional delay, power transmission, and data fidelity. We observe that the results from the t…
Stimulated Brillouin scattering (SBS) and Kerr-nonlinear four wave-mixing (FWM) are among the most important and widely studied nonlinear effects in optical fibres. At high powers SBS can be cascaded producing multiple Stokes waves spaced by the Brillouin frequency shift. Here, we investigate the complex nonlinear interaction of the cascade of Stokes waves, generated in a Fabry-Perot chalcogenide fibre resonator through the combined action of SBS and FWM. We demonstrate the existence of parameter regimes, in which pump and Stokes waves attain a phase-locked steady state. Real-time measurements…
We investigate the Relative Intensity Noise (RIN) properties of a multi-Stokes Brillouin fiber ring laser. We experimentally analyse intensity noise of each Stokes waves and study the noise dynamics of the cascaded Brillouin scattering process. We observe up to 20 dB/Hz intensity noise reduction compared to that of the RIN input pump laser. We examine the impact of the fiber ring quality factor on the laser RIN features such as amplitude reduction and relaxation frequency. A numerical model based on a set of coupled-mode equations replicate the experimental observations; confirming the class B…
Phase conjugation with stimulated Brillouin scattering can be used to correct wavefront aberrations in high-power laser systems. Here, we consider such process with cylindrical vector lasers beams. By using a vectorial approach and a modal decomposition, we obtain a differential matrix equation that enables the calculation of the structure of Stokes vector eigenmodes and their Brillouin gain. The emphasis is put on the mode with the largest gain, which contributes the most to the Stokes beam. We show that the phase conjugation of orbital angular momentum in cylindrical vector beams is prevente…
We predict and experimentally observe a nonlinear variant of stimulated Brillouin scattering in a single-mode fiber that arises from consideration of higher-order processes for phonon generation. The effect manifests itself at high laser excitation as the appearance of Stokes gain for a detuning equal to half of the conventional Brillouin frequency in the fiber, with no accompanying anti-Stokes absorption at the opposite detuning, and requires counter-propagating pump beams for phase-matching. We believe that this could be a new nonlinear optical effect that has not been observed before.
In order to explain pump depletion in Stimulated Brillouin scattering (SBS), coupled intensity equations describing the interaction of pump and stokes waves in Brillouin medium, must be solved simultaneously. Since this problem has well-defined boundary conditions, such a mathematical problem is known as the two-point boundary value problem. Conventional solution techniques leads transcendental equation which results implicit solution. In this paper, we accurately define Pump and Stokes evolution in lossless medium in terms of conserved quantity and proposed the solution of this conserved quan…
The coherent interaction between optical and acoustic waves via stimulated Brillouin scattering (SBS) is a fundamental tool for manipulating light at GHz frequencies. Its narrowband and noise-suppressing characteristics have recently enabled microwave-photonic functionality in integrated devices based on chalcogenide glasses, silica and silicon. Diamond possesses much higher acoustic and bandgap frequencies and superior thermal properties, promising increased frequency, bandwidth and power; however, fabrication of low-loss optical and acoustic guidance structures with the resonances matched to…
Stimulated Brillouin scattering with both pump and Stokes beams in resonance with whispering gallery modes of an ultra high Q CaF_2 resonator is demonstrated for the first time. The resonator is pumped with 1064 nm light and has a Brillouin lasing threshold of 3.5 microwatt. Potential applications include optical generation of microwaves and sensitive gyros.
We theoretically and numerically study the effects of thermal noise on pulses in backwards Stimulated Brillouin Scattering (SBS). Using a combination of stochastic calculus and numerical methods, we derive a theoretical model that can be used to quantitatively predict noise measurements. We study how the optical pulse configuration, including the input powers of the pump and Stokes fields, pulse durations and interaction time, affects the noise in the output Stokes field. We investigate the effects on the noise of the optical loss and waveguide length, and we find that the signal-to-noise rati…
Stimulated Brillouin scattering (SBS) has many applications, for example, in sensing, microwave photonics and signal processing. Here we report the first experimental study of SBS in chiral photonic crystal fiber (PCF), which displays optical activity and robustly maintains circular polarization states against external perturbations. As a result, circularly polarized pump light is cleanly back-scattered into a Stokes signal with the orthogonal circular polarization state, as is required by angular momentum conservation. By comparison, untwisted PCF generates a Stokes signal with an unpredictab…
We report the superluminal phenomenon of both Stokes and pump light in stimulated Brillouin scattering (SBS) via an optical-fiber ring lasing resonator. In our experiment, the superluminal generation of Stokes light firstly delayed with 33.79 ns and then propagated with the advancement of 93.34 ns within an 8-m single mode fiber (SMF), when the pump power increased from the SBS threshold to a higher power. This proves the first evidence that the optical interaction is determined by the group velocity even at the negative group velocity superluminal propagation. It is important that, this impli…
Stimulated Brillouin interactions mediate nonlinear coupling between photons and acoustic phonons through an optomechanical three-wave interaction. Though these nonlinearities were previously very weak in silicon photonic systems, the recent emergence of new optomechanical waveguide structures have transformed Brillouin processes into one of the strongest and most tailorable on-chip nonlinear interactions. New technologies based on Brillouin couplings have formed a basis for amplification, filtering, and nonreciprocal signal processing techniques. In this paper, we demonstrate strong guided-wa…
Stimulated Brillouin scattering (SBS) in low-power and compact microresonators has created a new field in cavity nonlinear photonics due to the marriage between acoustic and optical signal processing. Considering the fundamental differences between backward SBS and forward SBS processes, it is challenging to observe the coexistence of both processes in the same microresonator, as well as the photon noise suppression for the forward stimulated Brillouin laser (FSBL). In this paper, we demonstrate the first 20-dB-noise-squeezed FSBL generation excited by the coexisting backward SBL (BSBL) in an …
We analyze how to exploit Brillouin scattering for the purpose of cooling opto-mechanical devices and present a quantum-mechanical theory for Brillouin cooling. Our analysis shows that significant cooling ratios can be obtained with standard experimental parameters. A further improvement of cooling efficiency is possible by increasing the dissipation of the optical anti-Stokes resonance.
We investigate slow-light via stimulated Brillouin scattering in a room temperature optical fiber that is pumped by a spectrally broadened laser. Broadening the spectrum of the pump field increases the linewidth $Δω_p$ of the Stokes amplifying resonance, thereby increasing the slow-light bandwidth. One physical bandwidth limitation occurs when the linewidth becomes several times larger than the Brillouin frequency shift $Ω_B$ so that the anti-Stokes absorbing resonance cancels out substantially the Stokes amplifying resonance and hence the slow-light effect. We find that partial overlap of the…
Brillouin scattering is not usually considered as a mechanism that can cause cooling of a material due to the thermodynamic dominance of Stokes scattering in most practical systems. However, it has been shown in experiments on resonators that net phonon annihilation through anti-Stokes Brillouin scattering can be enabled by means of a suitable set of optical and acoustic states. The cooling of traveling phonons in a linear waveguide, on the other hand, could lead to the exciting future prospect of manipulating unidirectional phonon fluxes and even the nonreciprocal transport of quantum informa…
We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions…
The properties of space-time modulated media operating in the sub-sonic regime are discussed based on rigorous Bloch-Floquet theory. A geometrical description in the frequency-wavenumber plane is developed to provide insight into the possible interactions and their nature. It is shown that the secular equation has a singularity, which results in a weak/passive second harmonic generation process. Additionally bandgaps arising from the strong/active parametric interaction between an incident wave and its space-time harmonic, result in an inelastic Brillouin like scattering process. Hence when th…
Forward stimulated Brillouin scattering (F-SBS) is a third-order nonlinear-optical mechanism that couples between two co-propagating optical fields and a guided acoustic mode in a common medium. F-SBS gives rise to nonlinear wave mixing along optical fibers, which adds up with four-wave mixing induced by the Kerr effect. In this work, we report the distributed mapping of nonlinear wave mixing processes involving both mechanisms along standard single-mode fiber, in analysis, simulation and experiment. Measurements are based on a multi-tone, optical time-domain reflectometry setup, which is high…
We consider a counter-intuitive regime of stimulated Brillouin scattering in which the pump wave absorbs the phase defects of the Stokes wave, yielding a nonlinear self-stabilisation of the acoustic wave and a narrowing of the acoustic spectrum
In the well-known stimulated Brillouin scattering (SBS) process, spontaneous acoustic phonons in materials are stimulated by laser light and scatter the latter into a Stokes sideband. SBS becomes more pronounced in optical fibers and has been harnessed to amplify optical signals and even achieve lasing. Exploitation of SBS has recently surged on integrated photonics platforms as simultaneous confinement of photons and phonons in waveguides leads to drastically enhanced interaction. Instead of being optically stimulated, coherent phonons can also be electromechanically excited with very high ef…
We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of Stimulated Brillouin Scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length and pump power, whereas fifth-order losses lead to a non-monotonic relationship. We define a figure of merit for material…
An analogous laser action of magnons would be a subject of interest and is crucial for the study of nonlinear magnons spintronics. Here, we demonstrate the magnon laser behavior based on Brillouin light scattering in a ferrimagnetic insulator sphere which supports optical whispering gallery modes and magnon resonances. We show that the excited magnon plays what has traditionally been the role of the Stokes wave and is coherently amplified during the Brillouin scattering process, making magnon laser possible. Furthermore, the stimulating excited magnon number increasing exponentially with the i…
Polarization-resolved measurement of forward volume spin waves by micro-focused Brillouin light scattering
CEITEC BUT, Brno University of Technology（Brno理工大学CEITEC中心）；Institute of Molecular Physics, Polish Academy of Sciences（波兰科学院分子物理研究所）；School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology（华中科技大学量子科学与工程研究院物理学院，引力与量子物理湖北省重点实验室）；Department of Materials Science and Engineering, Massachusetts Institute of Technology（麻省理工学院材料科学与工程系）；Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家研究中心）；Institute of Physical Engineering, Brno University of Technology（Brno理工大学物理工程学院）
Narrow linewidth visible light lasers are critical for atomic, molecular and optical (AMO) applications including atomic clocks, quantum computing, atomic and molecular spectroscopy, and sensing. Historically, such lasers are implemented at the tabletop scale, using semiconductor lasers stabilized to large optical reference cavities. Photonic integration of high spectral-purity visible light sources will enable experiments to increase in complexity and scale. Stimulated Brillouin scattering (SBS) is a promising approach to realize highly coherent on-chip visible light laser emission. While pro…
Optical refrigeration of solids holds tremendous promise for applications in thermal management. It can be achieved through multiple mechanisms including inelastic anti-Stokes Brillouin and Raman scattering. However, engineering of these mechanisms remains relatively unexplored. The major challenge lies in the natural unfavorable imbalance in transition rates for Stokes and anti-Stokes scattering. We consider the influence of anisotropic photonic density of states on Raman scattering and derive expressions for cooling in such systems. We demonstrate optimization of the Raman cooling figure of …
The laser cooling of vibrational states of solids has been achieved through photoluminescence in rare-earth elements, optical forces in optomechanics, and the Brillouin scattering light-sound interaction. The net cooling of solids through spontaneous Raman scattering, and laser refrigeration of indirect band gap semiconductors, both remain unsolved challenges. Here, we analytically show that photonic density of states (DoS) engineering can address the two fundamental requirements for achieving spontaneous Raman cooling: suppressing the dominance of Stokes (heating) transitions, and the enhance…
